Analysis of Scheduling Algorithms with Reservations

In this work, we analyze the problem of scheduling a set of independent jobs on a homogeneous parallel computer. This problem has been widely studied from both a theoretical perspective (complexity analysis, and predictability of scheduling algorithms) and practical side (schedulers in production systems). It is common for some processors of a cluster to become unavailable for a certain period of time corresponding to reservations. These reservations represent blocks of time and quantities of resources set assigned in advance for specific applications. We propose here to investigate the scheduling problem where there are restricted resource availabilities. Our main result is to provide a deep analysis for this problem (complexity, lower bounds and upper bounds) for several variants of list scheduling algorithms. More precisely, we show that the problem of scheduling with any reservations can not be approximated. This leads to the study of restricted versions of this problem where the amount of reservation is limited. Our analysis is based on an old bound of Graham for resource constraint list scheduling for which we propose a new simpler proof by considering the continuous version of this problem.